Context. The method of distance determination of eclipsing binaries consists in combining the radii of both components determined from spectro-photometric observations with their respective angular diameters derived from the surface brightness-color relation (SBC). However, the largest limitation of the method comes from the uncertainty on the SBC relation: about 2% for late-type stars (or 0.04 magnitude) and more than 10% for early-type stars (or 0.2 mag). Aims. The aim of this work is to improve the SBC relation for early-type stars in the −1 ≤ V − K ≤ 0 color domain, using optical interferometry. Methods. Observations of eight B-and A-type stars were secured with the VEGA/CHARA instrument in the visible. The derived uniform disk angular diameters were converted into limb darkened angular diameters and included in a larger sample of 24 stars, already observed by interferometry, in order to derive a revised empirical relation for O, B, A spectral type stars with a V − K color index ranging from −1 to 0. We also took the opportunity to check the consistency of the SBC relation up to V − K 4 using 100 additional measurements. Results. We determined the uniform disk angular diameter for the eight following stars: γ Ori, ζ Per, 8 Cyg, ι Her, λ Aql, ζ Peg, γ Lyr, and δ Cyg with V − K color ranging from −0.70 to 0.02 and typical precision of about 1.5%. Using our total sample of 132 stars with V − K colors index ranging from about −1 to 4, we provide a revised SBC relation. For late-type stars (0 ≤ V − K ≤ 4), the results are consistent with previous studies. For early-type stars (−1 ≤ V − K ≤ 0), our new VEGA/CHARA measurements combined with a careful selection of the stars (rejecting stars with environment or stars with a strong variability), allows us to reach an unprecedented precision of about 0.16 magnitude or 7% in terms of angular diameter. Conclusions. We derive for the first time a SBC relation for stars between O9 and A3, which provides a new and reliable tool for the distance scale calibration.

Context. The B-W method is used to determine the distance of Cepheids and consists in combining the angular size variations of the star, as derived from infrared surface-brightness relations or interferometry, with its linear size variation, as deduced from visible spectroscopy using the projection factor. The underlying assumption is that the photospheres probed in the infrared and in the visible are located at the same layer in the star whatever the pulsation phase. While many Cepheids have been intensively observed by infrared beam combiners, only a few have been observed in the visible. Aims. This paper is part of a project to observe Cepheids in the visible with interferometry as a counterpart to infrared observations already in hand. Methods. Observations of δ Cep itself were secured with the VEGA/CHARA instrument over the full pulsation cycle of the star. Results. These visible interferometric data are consistent in first approximation with a quasi-hydrostatic model of pulsation surrounded by a static circumstellar environment (CSE) with a size of θCSE = 8.9 ± 3.0 mas and a relative flux contribution of fCSE = 0.07 ± 0.01. A model of visible nebula (a background source filling the field of view of the interferometer) with the same relative flux contribution is also consistent with our data at small spatial frequencies. However, in both cases, we find discrepancies in the squared visibilities at high spatial frequencies (maximum 2σ) with two different regimes over the pulsation cycle of the star, φ = 0.0 − 0.8 and φ = 0.8 − 1.0. We provide several hypotheses to explain these discrepancies, but more observations and theoretical investigations are necessary before a firm conclusion can be drawn. Conclusions. For the first time we have been able to detect in the visible domain a resolved structure around δ Cep. We have also shown that a simple model cannot explain the observations, and more work will be necessary in the future, both on observations and modelling.